Integrated method of modeling and signal correction of borehole transient electromagnetic response for borehole wall coupling effect

Abstract

The application discloses a well transient electromagnetic response modeling and signal correction integrated method for well wall coupling effect, and comprises the following steps: 1) constructing a wellbore-stratum- abnormal body three-dimensional geometric model; 2) deducing electromagnetic field control equations based on time-domain Maxwell equations, and processing the interfaces in the wellbore-stratum-abnormal body three-dimensional geometric model in combination with tangential electric field and normal magnetic flux density continuity; 3) calculating response signals V well (t) and response signals V ideal (t) by using the FDTD method; 4) analyzing signal space-time and spectrum characteristics, calculating well wall effect difference ΔV(t) by using response signals V well (t) and response signals V ideal (t); 5) optimizing time-varying correction coefficient α(t), and correcting well transient electromagnetic response signals based on the time-varying correction coefficient α(t) and the well wall effect difference ΔV(t) to obtain corrected signals. The application can provide reliable data support for high-resolution inversion of stratum electrical parameters, realize rapid and accurate identification of complex underground abnormal bodies, and significantly improve the application effect and engineering practicability of the BTEM technology in the fields of oil and gas exploration, geothermal resource evaluation, mineral resource detection and deep geological survey.

Description

Technical Field

[0001] This invention relates to the field of geophysical exploration technology, specifically to an integrated method for modeling and signal correction of transient electromagnetic response in wellbore, addressing wellbore coupling effects. Background Technology

[0002] Borehole transient electromagnetic (BTEM) is a high-precision geophysical exploration technique based on the principle of electromagnetic induction. It involves transmitting transient electromagnetic pulses from the surface and receiving the formation response signals in a vertical shaft to deduce the formation's conductivity or resistivity distribution for reservoir identification, formation stratification, and physical property evaluation. However, in the downhole environment, metal casing (with conductivity σ...) c ≈10 6 S / m), non-uniform mud (conductivity σ) m (z) Variation with depth) and the coupling between well logging and surrounding strata, as well as anomalies, cause significant interference to the electromagnetic signal, resulting in a large deviation between the forward modeling signal and the actual measurement signal, thus affecting the accuracy of formation parameter inversion. Existing technologies have the following shortcomings:

[0003] Model simplification error: Traditional forward models often neglect the eddy current effect of the metal sleeve (J e =σE) or simplify it to an insulator, which fails to accurately simulate the three-dimensional eddy current distribution;

[0004] The mud effect is ignored: mud conductivity σ m The non-uniform distribution of (z) and its attenuation effect on the signal (related to the eddy current penetration depth δ) have not been fully quantified, especially in high-salinity mud environments;

[0005] Insufficient signal characteristic analysis: Existing methods do not systematically analyze the comprehensive impact of wellbore effects on signal characteristics (amplitude, phase, spectrum, spatial distribution), and lack targeted correction strategies;

[0006] Lack of correction mechanism: Existing technologies do not provide a signal correction method based on wellbore effect coupling, and the measured signal is difficult to use for high-precision inversion after being disturbed.

[0007] In summary, existing technologies are insufficient to meet the high-precision logging requirements under complex well conditions (such as deep wells, high-salinity mud, and thick casing). There is an urgent need for a signal correction method that considers wellbore effect coupling to provide theoretical and quantitative guidance for exploration. Summary of the Invention

[0008] The purpose of this invention is to provide an integrated method for modeling and correcting transient electromagnetic responses in wellbore for wellbore coupling effects, comprising the following steps:

[0009] 1) Construct a three-dimensional geometric model of the wellbore, formation, and anomaly;

[0010] 2) The control equations for the electric and magnetic fields are derived based on the Maxwell equations in the time domain. The interfaces in the three-dimensional geometric model of wellbore-formation-anomaly are processed by combining the continuity of tangential electric field and normal magnetic flux density to ensure the continuity of tangential electric field and normal magnetic flux density and avoid non-physical errors in the signal caused by interface discontinuity.

[0011] 3) The FDTD method is used to calculate the response signal V considering the wellbore effect. well (t) and the response signal V neglecting wellbore effect ideal (t);

[0012] 4) Analyze the spatiotemporal and spectral characteristics of the signal, and utilize the response signal V considering the wellbore effect. well (t) and the response signal V neglecting wellbore effect ideal (t) Calculate the wellbore effect difference ΔV(t);

[0013] 5) Optimize the time-varying correction coefficient α(t), and based on the time-varying correction coefficient α(t) and the wellbore effect difference ΔV(t), correct the transient electromagnetic response signal in the well to obtain the corrected signal.

[0014] Furthermore, the three-dimensional geometric model of the wellbore-formation-anomaly includes the metal casing, drilling mud, logging tools, and surrounding rock.

[0015] Furthermore, in the three-dimensional geometric model of the wellbore-formation-anomaly, the electrical conductivity σ of the metal casing... c ∈[0.5×10⁶, 1.5×10⁶] S / m, thickness is 0.01-0.04m;

[0016] Mud conductivity σ m (z)∈[0.05,6]S / m, and the number of modeling layers is in the range of 10-20;

[0017] The logging tool has a spiral coil radius of 0.03-0.07m, a number of turns of 5-30, an excitation current of 0.5-20A, and uses a dipole antenna;

[0018] Rock resistivity ρ f ∈[0.5,5000]Ω·m.

[0019] Furthermore, in step 2), the steps of deriving the control equations for the electric and magnetic fields based on Maxwell's equations in the time domain include:

[0020] 2.1) Construct the time-domain Maxwell's equations, namely:

[0021]

[0022] J e=σE,D=εE,B=μH, (3)

[0023] Where σ, ε, and μ are the conductivity, permittivity, and permeability, respectively, J e V is the volume current density; E is the electric field strength; B is the magnetic flux density; H is the magnetic field strength; D is the electric displacement vector; t is time.

[0024] 2.2) Considering the high conductivity characteristics, the eddy current control equation for the bushing is derived, namely:

[0025]

[0026] 2.3) Considering the conductivity distribution, the formation eddy control equation is derived, namely:

[0027]

[0028] 2.4) Define the boundary conditions of the interface, i.e. (the normal is a dot product, and the tangential is a multiplication).

[0029] n×(E1-E2)=0, (tangential electric field is continuous), (6)

[0030] n·(B1-B2)=0, (normal magnetic flux density is continuous), (7)

[0031] n·(D1-D2)=ρ s (8) (The normal point displacement is continuous, considering surface charge).

[0032] In the formula, n is the interface normal vector pointing from medium 2 to medium 1; E1 and E2 are the electric field strengths in medium 1 and medium 2, respectively; B1 and B2 are the magnetic induction in medium 1 and medium 2, respectively; D1 and D2 are the electric displacement vectors in medium 1 and medium 2, respectively; ρ s The free surface charge density;

[0033] 2.5) The volume current density J of the transmitting coil is obtained by using a time-domain excitation function. e To perform modeling, that is:

[0034]

[0035] I coil Let N be the total current flowing through the coil, N be the number of turns in the coil, A be the cross-sectional area of ​​the coil conductor, and e be the current through the coil. coil It is a unit vector along the direction of the coil.

[0036] 2.6) Based on the interface boundary conditions, the interface in the three-dimensional geometric model of wellbore-formation-anomaly is processed to clarify the physical properties and computational constraints of the interface.

[0037] Furthermore, in step 3), the FDTD method is used to calculate the response signal V considering the wellbore effect. well (t) and the response signal V neglecting wellbore effect ideal The steps of (t) include:

[0038] 3.1) A non-uniform Yee mesh was used to mesh the three-dimensional geometric model of the wellbore-formation-anomaly; the mesh size was Δx×Δy×Δz, and the eddy current penetration depth of each mesh was [value missing]. ω is the angular frequency;

[0039] 3.2) Introduce a perfectly matched layer to process the mesh boundary; wherein, the absorption coefficient σ of the perfectly matched layer... PML ∈[0.1,10]S / m, the thickness is the sum of the thicknesses of 12-25 grid cells;

[0040] 3.3) Parallel computation receives the response signal V considering wellbore effects. well (t) and the response signal V neglecting wellbore effect ideal (t).

[0041] Furthermore, the wellbore effect difference ΔV(t) is shown below:

[0042] ΔV(t)=V well (t)-V ideal (t). (10)

[0043] Furthermore, the output correction signal V corrected (t) is shown below:

[0044] V corrected (t)=V well (t)+α(t)·ΔV(t), (11)

[0045] Where α(t) is the time-varying correction coefficient, and its initial value is based on σ. c , σ m (z) and time-frequency characteristic analysis estimation.

[0046] Furthermore, the time-varying correction coefficient α(t) is obtained by optimization using the least squares method combined with Tikhonov regularization;

[0047] The optimization objectives are as follows:

[0048]

[0049] A signal correction system based on the method includes a geometric modeling module, a forward modeling module, a signal characteristic analysis module, a correction algorithm module, and a verification and output module.

[0050] The geometric modeling module generates a three-dimensional mesh model of the wellbore and formation.

[0051] The forward modeling module calculates the forward modeling signal based on the FDTD algorithm;

[0052] The signal characteristic analysis module extracts the spatiotemporal and spectral characteristics of the wellbore effect, generates a feature library, and provides the correction algorithm module with spatiotemporal and spectral characteristic data of the wellbore effect.

[0053] The correction algorithm module executes an iterative optimization algorithm and outputs a correction signal;

[0054] The verification and output module evaluates the correction effect.

[0055] The technical effects of this invention are undeniable, and its beneficial effects are as follows:

[0056] 1) Three-dimensional fully coupled forward model: For the first time, a full-element forward model integrating the eddy current effect of metal casing, the stratified characteristics of mud conductivity and the three-dimensional structural coupling mechanism of wellbore-formation-anomaly is proposed. Based on the time-domain Maxwell equations, multi-field coupling is realized to accurately simulate the propagation and response characteristics of signals.

[0057] 2) Comprehensive signal characteristic analysis: The system analyzes the spatiotemporal and spectral characteristics (amplitude attenuation, phase delay, spectral characteristics, spatial distribution) of transient electromagnetic signals by wellbore effects, quantifies the contribution of casing eddy currents and mud attenuation, and provides a theoretical basis for signal correction.

[0058] 3) Unified Boundary Condition Treatment: Design a unified method for treating electromagnetic boundary conditions (tangential electric field E) at the interface of "casing-mud-formation-anomaly". t Continuous, normal magnetic flux density B n (Continuous), overcoming the error of separate calculation of eddy current field and formation response field in traditional models;

[0059] 4) Quantitative signal correction: An iterative optimization correction method based on time-domain characteristic analysis is proposed, and a time-varying correction coefficient α(t) is introduced to eliminate wellbore interference;

[0060] 5) Engineering guidance value: It provides theoretical and quantitative guidance for complex well conditions (such as deep wells, high salinity mud, and variable thickness casing), significantly improves the accuracy of formation parameter inversion, and reduces exploration costs.

[0061] In summary, addressing the problem that existing technologies cannot effectively eliminate wellbore interference under complex well conditions, leading to BTEM signal distortion and affecting the accuracy of formation parameter inversion, this invention proposes a high-precision correction method for transient electromagnetic signals in wells based on coupled modeling of the wellbore, formation, and anomaly. By constructing a three-dimensional time-domain coupled forward model encompassing the casing, wellbore fluids (such as logging mud), logging tools, surrounding formation, and complex anomalies, the comprehensive influence mechanism of wellbore effects on signal amplitude, phase, spectral characteristics, and spatial distribution is systematically analyzed within the framework of Maxwell's equations. Based on the modeling and analysis results, a high-precision BTEM signal correction method is proposed to effectively suppress wellbore interference and restore the true formation response. This method can provide reliable data support for high-resolution inversion of formation electrical parameters, enabling rapid and accurate identification of complex underground anomalies, and significantly improving the application effect and engineering practicality of BTEM technology in oil and gas exploration, geothermal resource evaluation, mineral resource detection, and deep geological surveys. Attached Figure Description

[0062] Figure 1 A schematic diagram of a three-dimensional geometric model of the wellbore and formation, showing the geometric and electrical parameter distribution of the metal casing, mud stratification, logging tools, surrounding rock, and anomalies;

[0063] Figure 2 : FDTD mesh generation and electromagnetic boundary condition processing diagram, annotating Yee mesh, PML boundary and interface conditions (E t B n );

[0064] Figure 3 Signal characteristic analysis diagram, showing V well (t) and V ideal The time-domain amplitude and phase difference of (t);

[0065] Figure 4 Flowchart of signal correction method;

[0066] Figure 5 The time-frequency domain characteristic analysis diagram shows the spectral characteristics (0.005Hz–50Hz) and frequency attenuation distribution of the signal;

[0067] Figure 6 The calibration effect verification diagram shows the error curves between the signal before and after calibration and the theoretical response signal;

[0068] Figure 7 Schematic diagram of mud conductivity stratification model, showing σ m (z) The effect of depth variation on signal attenuation and its quantitative impact;

[0069] Figure 8The eddy current effect analysis diagram of the casing shows the relationship between the eddy current penetration depth δ and the signal amplitude attenuation. Detailed Implementation

[0070] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0071] Example 1:

[0072] See Figures 1 to 8 An integrated method for modeling and signal correction of transient electromagnetic response in wellbore to address wellbore coupling effects includes the following steps:

[0073] 1) Construct a three-dimensional geometric model of the wellbore, formation, and anomaly;

[0074] 2) Based on the time-domain Maxwell's equations, the control equations for the electric and magnetic fields are derived. The interfaces in the three-dimensional geometric model of wellbore-formation-anomaly are handled by combining the continuity of the tangential electric field and the normal magnetic flux density. This ensures the continuity of the tangential electric field and the normal magnetic flux density, and satisfies the boundary conditions of the time-domain Maxwell's equations at the interfaces in the three-dimensional geometric model of wellbore-formation-anomaly, thereby accurately simulating the propagation characteristics of the electromagnetic field.

[0075] Tangential electric field E at the interface t Discontinuity leads to an infinitely large vortex electromotive force at the interface. The abrupt change in conductivity σ at the interface induces a tangential electric field E. t and normal magnetic flux density B n The discontinuity (electromagnetic field distortion) occurs. If the interface treatment is ignored, the field quantity at the grid nodes in the calculation will not satisfy the continuity, resulting in the signal containing non-physical oscillation errors. If the interface discontinuity is not treated, the wellbore effect difference ΔV(t) includes both the actual physical effect and the non-physical error. The non-physical error ε in ΔV(t) non-phy (t) can be expressed as:

[0076]

[0077] Where δ grid For the grid size, δ must be satisfied. grid δ skin (Skin depth) A coarse mesh will amplify numerical dispersion at the interface. Δ σ The difference in conductivity on both sides of the interface represents the conductivity jump (Δ) at the casing-mud interface. σ ~10 6 This will cause discontinuities in the electric field, and the equivalent conductivity of the medium at the interface will decrease. (σi σ represents the conductivity inside the interface. o (Conductivity on the outer side of the interface). If not strictly handled, ΔV(t) will contain the content due to the grid discretization (δ). grid ) and conductivity jump (Δ σ Non-physical errors caused by boundary conditions. Continuity treatment of the interface ensures that the boundary conditions force the field quantities to satisfy Maxwell's equations at the interface, avoiding non-physical jumps.

[0078] This can effectively reduce non-physical errors in numerical calculations, ensuring the reliability of forward modeling signals and the accuracy of correction algorithms;

[0079] 3) The FDTD method is used to calculate the response signal V considering the wellbore effect. well (t) and the response signal V neglecting wellbore effect ideal (t);

[0080] 4) Analyze the spatiotemporal and spectral characteristics of the signal, and utilize the response signal V considering the wellbore effect. well (t) and the response signal V neglecting wellbore effect ideal (t) Calculate the wellbore effect difference ΔV(t);

[0081] 5) Optimize the time-varying correction coefficient α(t), and based on the time-varying correction coefficient α(t) and the wellbore effect difference ΔV(t), correct the transient electromagnetic response signal in the well to obtain the corrected signal.

[0082] Example 2:

[0083] An integrated method for modeling and signal correction of transient electromagnetic response in wellbore for wellbore coupling effect is provided. The technical content is the same as in Example 1. Furthermore, the three-dimensional geometric model of wellbore-formation-anomaly includes metal casing, mud, logging tools and surrounding rock.

[0084] Example 3:

[0085] An integrated method for modeling and signal correction of transient electromagnetic response in wellbore to address wellbore coupling effects, with technical content identical to any one of Examples 1-2, further comprising the following: in the three-dimensional geometric model of wellbore-formation-anomaly, the conductivity σ of the metal casing... c ∈[0.5×10⁶, 1.5×10⁶] S / m, thickness is 0.01-0.04m;

[0086] Mud conductivity σ m (z)∈[0.05,6]S / m, and the number of modeling layers is in the range of 10-20;

[0087] The logging tool has a spiral coil radius of 0.03-0.07m, a number of turns of 5-30, an excitation current of 0.5-20A, and uses a dipole antenna;

[0088] Rock resistivity ρ f ∈[0.5,5000]Ω·m.

[0089] Example 4:

[0090] An integrated method for modeling and signal correction of transient electromagnetic response in wellbore facing wellbore coupling effects, with technical content identical to any one of Examples 1-3, further comprising, in step 2), the step of deriving the control equations of the magnetic field based on the time-domain Maxwell's equations, including:

[0091] 2.1) Construct the time-domain Maxwell's equations, namely:

[0092]

[0093] J e =σE,D=εE,B=μH, (3)

[0094] Where σ, ε, and μ are the conductivity, permittivity, and permeability, respectively, J e V is the volume current density; E is the electric field strength; B is the magnetic flux density; H is the magnetic field strength; D is the electric displacement vector; t is time.

[0095] 2.2) Considering the high conductivity characteristics, the eddy current control equation for the bushing is derived, namely:

[0096]

[0097] 2.3) Considering the conductivity distribution, the formation eddy control equation is derived, namely:

[0098]

[0099] 2.4) Define the boundary conditions of the interface, i.e. (the normal is a dot product, and the tangential is a multiplication).

[0100] n×(E1-E2)=0, (tangential electric field is continuous), (6)

[0101] n·(B1-B2)=0, (normal magnetic flux density is continuous), (7)

[0102] n·(D1-D2)=ρ s (8) (The normal point displacement is continuous, considering surface charge).

[0103] In the formula, n is the interface normal vector pointing from medium 2 to medium 1; E1 and E2 are the electric field strengths in medium 1 and medium 2, respectively; B1 and B2 are the magnetic induction in medium 1 and medium 2, respectively; D1 and D2 are the electric displacement vectors in medium 1 and medium 2, respectively; ρ s The free surface charge density;

[0104] 2.5) The volume current density J of the transmitting coil is obtained by using a time-domain excitation function. e To perform modeling, that is:

[0105]

[0106] I coil Let N be the total current flowing through the coil, N be the number of turns in the coil, A be the cross-sectional area of ​​the coil conductor, and e be the current through the coil. coil Let be a unit vector along the direction of the coil. This formula describes the average volumetric current density inside the coil conductor, assuming the current is uniformly distributed across the conductor's cross-section.

[0107] 2.6) Based on the interface boundary conditions, the interface in the three-dimensional geometric model of wellbore-formation-anomaly is processed to clarify the physical properties and computational constraints of the interface.

[0108] The location of the interfaces of the wellbore-formation-anomaly three-dimensional geometric model (such as the interface between the casing and the mud, the interface between the mud and the formation, and the interface between the formation and the anomaly) is essentially determined by the geometric structure of the model: the thickness of the casing, the spatial range of the mud, the boundary of the formation, etc., have been defined by geometric parameters (such as size, shape, and spatial coordinates) in step 1 "Constructing the three-dimensional geometric model".

[0109] Processing the interfaces in the 3D geometric model of the wellbore-formation-anomaly involves associating the interface boundary conditions defined in step 2.4 (tangential electric field continuity, normal magnetic flux density continuity, etc.) and the volume current density (current distribution of the transmitting coil) modeled in step 2.5 with the existing interfaces in the model. This clarifies which geometric boundaries belong to "interfaces" (i.e., the junctions of different media); the electromagnetic field continuity conditions (boundary conditions) that must be satisfied on these interfaces; and the spatial relationship between the volume current density (transmitting coil) and the interfaces (e.g., whether the coil is close to the casing-mud interface, and how the electromagnetic field generated by its current propagates and reflects at the interface). In short, "labeling" is to "attach physical labels" to the interfaces in the geometric model to ensure that boundary conditions can be correctly applied at these locations during subsequent numerical calculations (such as FDTD), avoiding non-physical jumps in field quantities, while also considering the influence of the transmitting coil current on the electromagnetic field at the interfaces.

[0110] In summary, step 1 constructs the geometric model and determines the spatial location (geometric properties) of the interface; step 2.4 defines the physical constraints (boundary conditions) that the interface must satisfy; step 2.5 clarifies the distribution of the field source (volume current density); and step 2.6 links the "geometric location," "physical constraints," and "field source influence" to provide a clear basis for interface processing in the subsequent FDTD calculation (step 3), ensuring that the calculation of the field quantity at the interface conforms to Maxwell's equations.

[0111] Example 5:

[0112] An integrated method for modeling and correcting transient electromagnetic responses in wells considering wellbore coupling effects is provided. The technical content is the same as any one of Examples 1-4. Further, in step 3), the FDTD method is used to calculate the response signal V considering the wellbore effect. well (t) and the response signal V neglecting wellbore effect ideal The steps of (t) include:

[0113] 3.1) A non-uniform Yee mesh was used to mesh the three-dimensional geometric model of the wellbore-formation-anomaly; the mesh size was Δx×Δy×Δz, and the eddy current penetration depth of each mesh was [value missing]. ω is the angular frequency;

[0114] 3.2) Introduce a perfectly matched layer to process the mesh boundary; wherein, the absorption coefficient σ of the perfectly matched layer... PML ∈[0.1S / m,10S / m], the thickness is the sum of the thicknesses of 12-25 grid cells;

[0115] 3.3) Parallel computation receives the response signal V considering wellbore effects. well (t) and the response signal V neglecting wellbore effect ideal (t).

[0116] Example 6:

[0117] An integrated method for modeling and signal correction of transient electromagnetic response in wellbore to address wellbore coupling effects is provided, with the technical content identical to any one of Examples 1-5. Furthermore, the wellbore effect difference ΔV(t) is shown below:

[0118] ΔV(t)=V well (t)-V ideal (t). (1)

[0119] Example 7:

[0120] An integrated method for modeling and signal correction of transient electromagnetic response in wellbore to address wellbore coupling effects, with technical content identical to any one of Examples 1-6, further comprising the output correction signal V. corrected (t) is shown below:

[0121] V corrected (t)=V well (t)+α(t)·ΔV(t), (1)

[0122] Where α(t) is the time-varying correction coefficient, and its initial value is based on σ. c , σ m (z) and time-frequency characteristic analysis estimation.

[0123] Example 8:

[0124] An integrated method for modeling and signal correction of transient electromagnetic response in wellbore for wellbore coupling effect, with the same technical content as any one of Examples 1-7, further wherein the time-varying correction coefficient α(t) is obtained by least squares method combined with Tikhonov regularization optimization;

[0125] The optimization objectives are as follows:

[0126]

[0127] Example 9:

[0128] A signal correction system based on the method described in any one of Embodiments 1-8 includes a geometric modeling module, a forward modeling module, a signal characteristic analysis module, a correction algorithm module, and a verification and output module;

[0129] The geometric modeling module generates a three-dimensional mesh model of the wellbore and formation.

[0130] The forward modeling module calculates the forward modeling signal based on the FDTD algorithm;

[0131] The signal characteristic analysis module extracts the spatiotemporal and spectral characteristics of the wellbore effect, generates a feature library, provides spatiotemporal and spectral characteristic data of the wellbore effect for the correction algorithm module, and supports iterative optimization algorithms to generate accurate correction signals.

[0132] The correction algorithm module executes an iterative optimization algorithm and outputs a correction signal;

[0133] The verification and output module evaluates the correction effect.

[0134] Example 10:

[0135] A method for correcting transient electromagnetic signals in a well considering wellbore effect coupling includes the following steps:

[0136] Construct a three-dimensional geometric model of the wellbore-formation-anomaly, including the metal casing, drilling mud, logging tools, and surrounding rock;

[0137] The control equations for the electric and magnetic fields are derived based on Maxwell's equations in the time domain, and the interface is treated by combining the continuity of the tangential electric field and the normal magnetic flux density.

[0138] Calculating the forward modeling signal V using the FDTD method well (t) and the ideal signal V ideal (t);

[0139] Analyze the spatiotemporal and spectral characteristics of the signal and calculate the wellbore effect difference ΔV(t);

[0140] Optimize the time-varying correction coefficient α(t) and output the correction signal V.corrected (t)=V well (t)+α(t)·ΔV(t).

[0141] The wellbore effect includes a coupling of the metal casing eddy current effect and the mud conductivity stratification effect, with the eddy current penetration depth being...

[0142] Signal characteristics include time-domain amplitude attenuation, phase delay, frequency-domain attenuation factor, and spatial distribution. Time-frequency distribution features are extracted through S-transform.

[0143] The correction coefficient α(t) is optimized using the least squares method combined with Tikhonov regularization, with a convergence threshold of 10. -5 The regularization parameter λ∈

[10] -4 10 -2 ];

[0144] The method supports complex well conditions such as deep wells, high-salinity mud, and variable-thickness casing; Example 11:

[0145] A method for correcting transient electromagnetic signals in a well considering wellbore effect coupling includes the following steps:

[0146] Construct a three-dimensional geometric model of the wellbore and formation, such as Figure 1 The above, Figure 1 This diagram illustrates a 3D geometric model of the wellbore-formation system, detailing the geometric and electrical parameter distributions of the casing, mud layers, logging tools, surrounding rock, and anomalies. The wellbore structure penetrates multiple formations, and the casing and mud layers are labeled with their spatial locations and electrical properties (such as resistivity), reflecting the geometric modeling module's ability to generate a 3D mesh model of the wellbore-formation system. The logging tools are located within the well, and their relative positions to anomalies are indicated, providing a model foundation for the forward modeling module to calculate forward signals based on the FDTD algorithm. The electrical parameter distributions of the surrounding rock and anomalies are distinguished by different colors or textures, intuitively supporting the signal characteristic analysis module in extracting the spatiotemporal and spectral characteristics of wellbore effects. The overall layout, through the combination of 3D geometry and electrical parameters, clearly presents the physical background of transient electromagnetic forward modeling and the data correlation between modules of the signal correction system.

[0147] Geometric definition: Establish a system containing a metal sleeve (conductivity σ) c ∈[0.5×10⁶, 1.5×10⁶] S / m, thickness 0.01-0.04m), mud (conductivity σ) m (z)∈[0.05,6]S / m, modeled in 10-20 layers), logging tools (spiral coil radius 0.03-0.07m, number of turns 5-30, excitation current 0.5-20A, dipole antenna) and surrounding rock (resistivity ρ fGeometric model of (∈[0.5,5000]Ω·m);

[0148] Modeling tools: Use 3D modeling software (such as Gmsh, COMSOL) to define geometric boundaries, electrical parameters, and volume current density J. e It supports the generation of non-uniform meshes;

[0149] Parameter input: Input well condition data (such as casing thickness, mud salinity, formation resistivity, etc.) through the parameterized interface to ensure model adaptability.

[0150] Derivation of the governing equations for the electric and magnetic fields:

[0151] Fundamental equations: Based on the time-domain Maxwell's equations:

[0152]

[0153] J e =σE,D=εE,B=μH, (3)

[0154] Where σ, ε, and μ are the conductivity, permittivity, and permeability, respectively, J e The volume current density.

[0155] Sleeve: Considering its high conductivity characteristics, the eddy current control equation is derived:

[0156]

[0157] Displacement current is ignored (ε≈0) to simplify the calculation.

[0158] Formation: Considering the conductivity distribution:

[0159]

[0160] Define the boundary conditions of the interface, i.e. (the normal is a dot product, and the tangential is a multiplication).

[0161] n×(E1-E2)=0, (tangential electric field is continuous), (1)

[0162] n·(B1-B2)=0, (normal magnetic flux density is continuous), (2)

[0163] n·(D1-D2)=ρ s (3) (The normal point displacement is continuous, and surface charge is considered.)

[0164] Excitation: Modeling the volume current density J of the transmitting coil e The time-domain excitation function (rectangular pulse, width 10) is adopted. -6 -10 - 4 s).

[0165] Discrete solution of FDTD:

[0166] Mesh generation: A non-uniform Yee mesh is used, with mesh sizes Δx, Δy, Δz ∈ [0.004, 0.06] m, satisfying the electromagnetic wavelength and eddy current penetration depth requirements. Total grid count: 10-30 million;

[0167] Boundary treatment: Introduce a perfectly matched layer (PML, thickness 12-25 mesh elements, absorption coefficient σ) PML ∈[0.1,10]S / m), suppress artificial reflections;

[0168] Parallel computing: GPU acceleration is used, multi-core parallel solving is supported, and the time for a single simulation is controlled within 1-5 hours;

[0169] Output: The induced electromotive force V generated by the receiving coil well (t)(considering wellbore effect) and V ideal (t)(ignoring wellbore effect).

[0170] Figure 2 This diagram illustrates the geometric modeling and forward modeling module of a signal correction system based on the FDTD algorithm. In the diagram, the PML (Perfect Matching Layer) boundary conditions and the Yee mesh structure are used to simulate a three-dimensional mesh model of the wellbore-formation. The blue area represents an example of mesh generation, demonstrating the meshing capability of the geometric modeling module. The Yee mesh, combined with the electric field (E), magnetic field (H), electric displacement (D), and magnetic induction (B) parameters from Maxwell's equations, reflects the spatial distribution and interrelationships of field quantities during the transient electromagnetic three-dimensional forward modeling calculation. The forward modeling module, based on the FDTD algorithm, generates forward modeling signals through mesh generation and parameter iteration, providing a foundation for the signal characteristic analysis module to extract the spatiotemporal and spectral characteristics of wellbore effects. The overall layout, through the combination of the three-dimensional mesh and the parameters of Maxwell's equations, intuitively presents the transient electromagnetic forward modeling process.

[0171] Analyze signal characteristics:

[0172] Figure 3 A signal characteristic analysis diagram is presented, which details the characteristics of the ideal signal V. ideal With the actual voltage signal V inside the well well The difference in amplitude and phase in the time domain. The upper part of the figure shows the amplitude curve, V. ideal (Black curve) and V well (The red curve) shows an exponential decay trend over time (0 to 10 ms), but V well The amplitude was significantly lower than V idealThis indicates that the wellbore effect causes signal energy loss. The lower part of the figure shows the phase difference curve, with a large initial phase difference (about 4 degrees) that decreases and stabilizes over time, reflecting the time-domain delay effect of the wellbore effect on signal propagation. In summary, the wellbore effect significantly weakens the signal amplitude through scattering and absorption, and introduces phase shift, thereby interfering with the accuracy of transient electromagnetic signals, providing an optimization basis for the correction algorithm module.

[0173] Time-domain analysis: Extracting V well (t) and V ideal The amplitude decay (5-20%) and phase delay (0.05-0.2ms) of (t) are quantified to reflect the wellbore effect;

[0174] Figure 5 This paper presents a time-frequency domain characteristic analysis diagram based on the S-transform, analyzing the signal V. ideal and V well Spectral characteristics and frequency attenuation distribution within the 0.005-50Hz frequency range. Figure 5 (a) Presents V ideal The time-frequency characteristic distribution shows that its initial spectral energy distribution decays uniformly over time. Figure 5 (b) Show V well The time-frequency characteristic distribution shows that the spectral energy is significantly weakened and the low-frequency components decay faster, reflecting the energy loss caused by the wellbore effect. Figure 5 (c) indicates that V well With V ideal The differences in time-frequency characteristics are mainly manifested in the significant attenuation of high-frequency components and phase shift, revealing that the wellbore effect interferes with signal propagation through scattering and absorption mechanisms. The experimental analysis concludes that the wellbore effect significantly alters the time-frequency characteristics of the signal, verifying that the signal correction system needs to be optimized for spectral attenuation and phase shift, providing important technical evidence for the design of the correction algorithm module.

[0175] Time-frequency domain analysis: The attenuation factor and spectral characteristics were extracted by using the S-transform algorithm (frequency range 0.005-50Hz) to identify the contributions of casing eddy current (peak frequency 1-10Hz) and mud attenuation (low frequency dominant).

[0176] Spatial distribution: Analysis of the spatial attenuation of the signal at the wellbore-formation interface (with σ) m (z) Related to casing thickness

[0177] Difference calculation:

[0178] ΔV(t)=V well (t)-V ideal (t). (9)

[0179] Sensitivity analysis: assessing σ c , σ mThe influence of (z) on ΔV(t) was investigated to construct a wellbore effect feature library.

[0180] Signal correction algorithm:

[0181] Correction model:

[0182] V corrected (t)=V well (t)+α(t)·ΔV(t), (10)

[0183] Where α(t) is the time-varying correction coefficient, and its initial value is based on σ. c , σ m (z) and time-frequency characteristic analysis estimation.

[0184] Figure 6 The diagram shows the verification effect of the correction, used to compare the time-domain characteristics and dynamic error distribution of the signal before and after correction with the theoretical response signal. The left diagram presents V. ideal (Green), V well (Red) and V corrected The three blue curves show the correction signal V. corrected Compared to V well Closer to the theoretical response V ideal This verifies the optimization effect of the correction algorithm. The right figure shows the dynamic error curve, which quantifies the residual change during the correction process. It indicates that the error is relatively large in the initial stage (significant peak) but tends to stabilize over time, reflecting the effectiveness of the correction process. The error percentage is calculated as (|V corrected -V ideal | / V ideal The experimental results, calculated at 100%, showed that the average error after correction was reduced to below 5%, significantly lower than the over 20% error of the uncorrected signal. The conclusion is that the correction algorithm significantly reduces the signal deviation caused by the wellbore effect, providing experimental evidence for the reliability and practicality of the signal correction system.

[0185] Optimization algorithm:

[0186]

[0187] Use Tikhonov regularization (regularization parameter λ∈

[10] ). -4 10 -2 ]), convergence threshold 10 -5 .

[0188] Iterative process: Gradient descent method is used, and the algorithm is iterated 10-25 times to optimize α(t) and ensure that the signal matching degree reaches the expected effect;

[0189] Adaptive adjustment: λ is dynamically adjusted according to well conditions (such as mud salinity and casing thickness) to improve correction robustness.

[0190] Verification and Engineering Applications:

[0191] Synthetic validation: The correction effect is validated using synthetic datasets (casing, mud, formation) with known parameters, and the signal error is quantitatively evaluated;

[0192] Guidance output: Generates wellbore effect characteristic reports and parameter optimization suggestions to provide quantitative guidance for exploration.

[0193] Example 12:

[0194] A signal correction system based on the method described in any one of Embodiments 1-11, characterized in that it includes a geometric modeling module, a forward modeling module, a signal characteristic analysis module, a correction algorithm module, and a verification and output module.

[0195] Geometric modeling module: Generates a 3D mesh model of the wellbore and formation, supporting parametric input (casing thickness, mud conductivity, tool geometry parameters);

[0196] Forward Response Calculation Module: Calculates forward signals based on the FDTD algorithm, supporting GPU parallel acceleration (NVIDIA CUDA);

[0197] Signal Characteristic Analysis Module: Extracts the spatiotemporal and spectral characteristics (amplitude, phase, spectrum, spatial distribution) of wellbore effect and generates a feature library;

[0198] Correction algorithm module: Executes iterative optimization algorithm, outputs correction signal, and integrates adaptive regularization;

[0199] Verification and Output Module: Evaluate the correction effect and guide exploration.

[0200] This invention achieves, for the first time, quantitative identification and correction of wellbore effects through three-dimensional coupled forward modeling and comprehensive signal characteristic analysis;

[0201] This invention systematically reveals the comprehensive influence of wellbore structure on the time, frequency, and spatial distribution characteristics of signals, providing a theoretical basis for inversion algorithm optimization and exploration design;

[0202] This invention is suitable for complex well conditions such as deep wells, high-salinity mud, and variable-thickness casing, improves the accuracy of formation parameter inversion, and fills the gap in transient electromagnetic signal correction technology in complex wells.

[0203] For example, Figure 7(a) illustrates the vertical distribution of conductivity in the wellbore and surrounding mud region. The well environment is divided into three layers: ① Top of the mud layer, with low conductivity (σ≈0.05S / m), indicating poor conductivity in the mud region near the wellhead, possibly due to low mud concentration, low solid content, or fewer impurities. ② Middle layer, where signal attenuation accelerates with depth. The conductivity gradually increases with depth (0.1~0.5S / m), indicating increased electrolyte concentration and conductive particle content at deeper depths, possibly due to mud settling, self-weight compaction, and accumulation of mud contaminants. ③ Bottom layer, with the highest conductivity (σ≈1.0S / m or even higher), corresponding to the densest mud, lowest water content, and highest ionization. This region has the most significant damping effect on electromagnetic wave propagation and is the key control layer for signal attenuation. This layering characteristic reveals that mud conductivity gradually increases with depth, reflecting the direct influence of the vertically non-uniform conductive structure on electromagnetic field transmission characteristics.

[0204] Figure 7 (b) shows the mud conductivity σ m (z) The effect of depth variation on the decay behavior of transient electromagnetic signal amplitude over time. The curves in the figure represent the decay process of the induced voltage received by the receiving coil in the well over time under different mud conductivity distributions. The inset is a magnified view of the initial response. As can be seen from the figure, with σ... m As (z) increases, the rate of decrease in induced voltage accelerates significantly. This is because high-conductivity media have a stronger ability to dissipate induced current and a faster eddy current decay rate, resulting in a more rapid decrease in detectable induced voltage. After 1 ms, the amplitude curves for different conductivities show increasingly pronounced bifurcation. This indicates that in the later response stage, the conductivity of the mud has a more significant impact on the secondary induction field, and special attention should be paid to the acquisition and interpretation of signals in this section.

[0205] Figure 8 (a) is a concise yet information-rich schematic diagram of the eddy current response of a metal casing. Arrows, text, and structural morphology illustrate the interference mechanism of the metal casing on TEM signals. The casing is a hollow metal cylinder placed inside a wellbore. An excitation coil applies a pulsed current in transient electromagnetic methods, generating a time-varying magnetic field. This time-varying magnetic field passes through the highly conductive metal casing, inducing annular eddy currents within its walls. The circular red arrows within the casing indicate the direction of the eddy currents, following Lenz's law and moving in the opposite direction to the changing trend of the excitation magnetic field. The eddy currents are mainly concentrated near the region where the excitation magnetic field changes most drastically, and their intensity rapidly decreases from the outside in—a typical eddy current shielding effect. The diagram emphasizes that the stronger the eddy current, the greater the signal amplitude attenuation; the deeper the eddy current penetration, the smaller the amplitude attenuation. The metal casing significantly shields or attenuates transient electromagnetic signals, especially at higher signal frequencies or when the casing conductivity is high.

[0206] Figure 8(b) is a quantitative analysis graph, with the horizontal axis representing the eddy current penetration depth δ (unit: meters) and the vertical axis representing the normalized induced voltage (unit: mV / δ), using a semi-logarithmic coordinate system (logarithmic scale on the vertical axis).

[0207] Considering the response of a vertical magnetic dipole source in a homogeneous medium (i.e., the z-coil commonly used for well probing), the voltage decay exhibits the following time-domain behavior.

[0208]

[0209] This expression shows that the voltage decays rapidly over time and is strongly affected by shielding (such as bushings) in a short period of time.

[0210] Eddy current penetration depth describes the distance an alternating electromagnetic field attenuates in a conductor, defined as the depth required for the magnetic field to decay to 1 / e of its original strength. Its time-domain expression is:

[0211]

[0212] Let's express time as penetration depth:

[0213]

[0214] Substituting (3) into (1) yields:

[0215]

[0216] Therefore, draw Figure 8 (b) is a quantitative analysis graph, with the horizontal axis representing the eddy current penetration depth δ (unit: meters) and the vertical axis representing the normalized induced voltage (unit: mV / δ), using a semi-logarithmic scale (logarithmic scale on the vertical axis). The curve generally shows a clear negative exponential decay trend at smaller penetration depths (δ < 2 × 10⁻⁶). -2 The signal voltage amplitude dropped rapidly, indicating that the eddy current shielding was extremely strong.

[0217] As the penetration depth gradually increases (δ>4×10), -2 As the signal attenuation rate gradually slows down (m), it tends to stabilize. When it approaches its limit, the signal amplitude tends to be extremely low, but it will not be completely zero, indicating that some energy still penetrates.

[0218] This invention improves the quality of well logging data and the reliability of inversion, effectively reducing the risk of exploration misjudgment caused by signal distortion. According to preliminary assessment, it can save about 200,000 to 800,000 yuan in exploration and interpretation costs per well.

Claims

1. An integrated method for modeling and signal correction of transient electromagnetic response in wellbore facing wellbore coupling effects, characterized in that, Includes the following steps: Step 1) Construct a three-dimensional geometric model of the wellbore-formation-anomaly body; Step 2) Based on Maxwell's equations in the time domain, derive the control equations for the electric and magnetic fields, and combine the continuity of the tangential electric field and normal magnetic flux density to process the interface in the three-dimensional geometric model of wellbore-formation-anomaly, so as to avoid non-physical errors in the signal caused by the discontinuity of the interface. Step 3) Calculate the response signal considering wellbore effects using the FDTD method. and ignoring wellbore effect response signal ; Step 4) Analyze the spatiotemporal and spectral characteristics of the signal, and utilize the response signal considering the wellbore effect. and ignoring wellbore effect response signal Calculate the difference in wellbore effect ; Step 5) Optimize time-varying correction coefficients And based on time-varying correction coefficients Difference between wellbore effect and wellbore effect The transient electromagnetic response signal in the well is corrected to obtain the corrected signal; Step 2), the steps for deriving the control equations for the electric and magnetic fields based on Maxwell's equations in the time domain include: Step 2.1) Construct the time-domain Maxwell's equations, namely: （1） （2） （3） in , , These are electrical conductivity, permittivity, and magnetic permeability, respectively. V is the volume current density; E is the electric field strength; B is the magnetic flux density; H is the magnetic field strength; D is the electric displacement vector; t is time. Step 2.2) Considering the high conductivity characteristics, derive the eddy current control equation for the bushing, namely: （4） Step 2.3) Considering the conductivity distribution, derive the formation eddy current control equation, i.e.: （5） Step 2.4) Define the interface boundary conditions, namely: （6） （7） （8） In the formula, n is the interface normal vector pointing from medium 2 to medium 1; , The electric field strengths in dielectric 1 and dielectric 2; , The magnetic induction intensity in medium 1 and medium 2; , These are the electric displacement vectors in medium 1 and medium 2; The free surface charge density; Step 2.5) Use a time-domain excitation function to measure the volume current density of the transmitting coil. To perform modeling, that is: （9） In the formula, Let N be the total current flowing through the coil, N be the number of turns in the coil, and A be the cross-sectional area of ​​the coil conductor. It is a unit vector along the direction of the coil; Step 2.6) Based on interface boundary conditions and volume current density The interfaces in the three-dimensional geometric model of wellbore-formation-anomaly are processed to clarify the physical properties and computational constraints of the interfaces.

2. The integrated method for modeling and signal correction of transient electromagnetic response in wellbore oriented towards wellbore coupling effect as described in claim 1, characterized in that, The three-dimensional geometric model of the wellbore-formation-anomaly includes the metal casing, drilling mud, logging tools, and surrounding rock.

3. The integrated method for modeling and signal correction of transient electromagnetic response in wellbore oriented towards wellbore coupling effect as described in claim 2, characterized in that, In the three-dimensional geometric model of wellbore-formation-anomaly, the electrical conductivity of the metal casing. S / m, thickness 0.01 m–0.04 m; mud conductivity S / m, and the number of modeling layers ranges from 10 to 20; The logging tool has a spiral coil radius of 0.03 m–0.07 m, a number of turns range of 5–30, an excitation current range of 0.5 A–20 A, and uses a dipole antenna; Rock resistivity Ω · m.

4. The integrated method for modeling and signal correction of transient electromagnetic response in wellbore oriented towards wellbore coupling effect as described in claim 1, characterized in that, In step 3), the FDTD method is used to calculate the response signal considering the wellbore effect. and ignoring wellbore effect response signal The steps include: Step 3.1) The wellbore-formation-anomaly 3D geometric model is meshed using a non-uniform Yee mesh; where the mesh size is... The eddy current penetration depth of each grid is ; Angular frequency; Step 3.2) Introduce a perfectly matched layer to process the mesh boundaries; wherein, the absorption coefficient of the perfectly matched layer... S / m, thickness is the sum of the thicknesses of 12–25 grid cells; Step 3.3) Parallel computation to receive the response signal considering wellbore effects and ignoring wellbore effect response signal .

5. The integrated method for modeling and signal correction of transient electromagnetic response in wellbore oriented towards wellbore coupling effect as described in claim 1, characterized in that, Output correction signal As shown below: （10） in This is the time-varying correction factor.

6. The integrated method for modeling and signal correction of transient electromagnetic response in wellbore oriented towards wellbore coupling effect as described in claim 1, characterized in that, The time-varying correction coefficient α(t) is obtained by optimization using the least squares method combined with Tikhonov regularization; The optimization objectives are as follows: （11）。 7. A signal correction system based on the method of any one of claims 1-6, characterized in that, It includes a geometric modeling module, a forward modeling module, a signal characteristic analysis module, a correction algorithm module, and a verification and output module; The geometric modeling module generates a three-dimensional mesh model of the wellbore and formation. The forward modeling module calculates the forward modeling signal based on the FDTD algorithm; The signal characteristic analysis module extracts the spatiotemporal and spectral characteristics of the wellbore effect, generates a feature library, and provides the correction algorithm module with spatiotemporal and spectral characteristic data of the wellbore effect. The correction algorithm module executes an iterative optimization algorithm and outputs a correction signal; The verification and output module evaluates the correction effect.

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